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A Calibration of the 85 Peg Binary System

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A Calibration of the 85 Peg Binary System A&A 392, 529–533 (2002) Astronomy DOI: 10.1051/0004-6361:20020962 & c ESO 2002 Astrophysics A calibration of the 85 Peg binary system J. Fernandes1,P.Morel2, and Y. Lebreton3 1 Observat´orio Astron´omico da Universidade de Coimbra, Santa Clara, 3040 Coimbra, Portugal and Departamento de Matem´atica da Faculdade de Ciˆencias e Tecnologia da Universidade de Coimbra, Portugal 2 D´epartement Cassini, UMR CNRS 6529, Observatoire de la Cˆote d’Azur, BP 4229, 06304 Nice Cedex 4, France 3 GEPI, Observatoire de Paris Meudon, 92195 Meudon, France Received 28 September 2001 / Accepted 11 June 2002 Abstract. We have calibrated the initial abundances, age and mixing-length parameters of the visual binary system 85 Pegasi. We obtain an age t85 Peg = 9 345 500 Myr, masses mA = 0:88 0:01 M and mB = 0:55 0:02 M , an initial helium mass = : : Fe = − : : Λ = : : fraction Yi 0 25 0 01, an initial metallicity [ H ]i 0 185 0 054 and mixing-length parameters A 1 80 0 05 and ΛB = 2:14 0:10. We find that, as already proposed, 85 Peg B is itself a binary. The mass of the unseen companion is mb ≈ 0:11 M . Key words. stars: binaries: visual – stars: evolution – stars: fundamental parameters – stars: individual: 85 Peg 1. Introduction massive than 85 Peg A the brighter one (e.g. Slocum 1915; Hall 1948; Underhill 1963). This was found again by Martin & The calibration of a binary system is based on the adjustment Fe Mignard (1998) on the basis of Hipparcos observations. This of stellar modeling parameters (t?; Y ; [ ] ; Λ ; Λ ) to the ob- i H i A B abnormal situation could be explained by the fact that 85 Peg B servational data at the age t? of the system, with the reasonable is an undetected binary. 85 Peg A is known as a metal-poor star hypothesis of a common origin for both components (same ini- and found to be much older than the Sun (Perrin et al. 1977). tial chemical composition and age). Y and [ Fe ] are, respec- i H i Because of its small mass, 85 Peg A sits close to the zams Λ tively, the initial helium mass fraction and metallicity, A and which gives a constraint on its initial helium abundance, a Λ B are respectively the mixing-length parameters of the pri- value traditionally associated with primordial helium (Perrin mary A and secondary B. For each component one also infers et al. 1977; Catchpole et al. 1967; Smak 1960). a mass value consistent with theoretical stellar modeling. The photometry and the atmospheric parameters of Taking into account the most recent theoretical and 85 Peg A have been determined many times. The first spectro- observational astrometric, spectroscopic and photometric scopic determination of the metallicity is from Wallerstein & results we undertake the calibration of 85 Pegasi (HD 224930, Helfer (1959), while the most recent metallicity and effective HIP 171, BD+26 4734 4, HR 9088, β 733 ADS 17175, temperature determinations are due to van’t Veer (2000) and IDS 23569 +2633; α = 00h 02m 10s, δ =+27◦0405600 (2000)). Fulbright (2000). While 85 Peg A is a well known star, the sec- It is a well-known visual and single-lined spectroscopic binary ondary component is less well known. The greatest limitations system. The components, 85 Peg A and B, are main sequence to studying 85 Peg B in detail were the lack of individual photo- low mass stars of spectral types G5 and K7 respectively metric and spectroscopic measurements due to its proximity to (ten Brummelaar et al. 2000). The shortness of the period 85 Peg A (ρ ≈ 000: 75). Recently, ten Brummelaar et al. (2000), (≈27 years) and the proximity to the Sun (∼12 pc) give it an in- performed differential photometry in the Johnson vri system teresting place among the binary stars. The visual orbit is very for both stars using adaptative optics, which allows us to deter- well known (Hall 1948). Nevertheless, some studies of the or- mine the effective temperatures and bolometric magnitudes of bit have been recently published. The latest (S¨oderhjelm 1999) both components. has yielded improvements to the Hipparcos trigonometric parallax and orbit, combining data from the satellite with In their pioneering work Fernandes et al. (1998) tried to ground-based observations. 85 Peg is one of the rare cases calibrate the helium abundance and age of both 85 Peg A and for which the mass ratio can be obtained by both astrometric B by means of stellar models. No solution was possible when and spectroscopic observations. For many years investigators fitting both components for the same helium and age values. have claimed that 85 Peg B, the fainter component, is more The models appeared to be hotter than the observations. The discrepancy appears to be removed if the microscopic diffusion Send offprint requests to: J. Fernandes, of helium and heavy elements, the enrichment of α-elements e-mail: [email protected] and the non-lte effects in the iron abundances determinations Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20020962 530 J. Fernandes et al.: Improved calibration of 85 Peg Table 1. Relevant orbital elements of the 85 Peg. As usual P is the orbital period in years, a the semi-major axis, i the inclination and e the eccentricity. The error bars are probable errors. S¨oderhjelm does not give the errors on the orbital elements but he indicates that the number of given decimals reflect the mean errors. Author Paie Hall (1948) 26:27 0:19 000: 83 000: 02 −50◦:0 2◦:00:38 0:01 S¨oderhjelm (1999) 26:28 000: 83 −49◦: 0:38 are taken into account in models of low mass stars (Lebreton the adopted orbital elements and parallax, we derive the “spec- et al. 1999). Nevertheless, Lebreton et al. did not perform a troscopic” mass fraction: full calibration of 85 Peg A and did not examine the secondary B = 0:43 0:06: component. s Our purpose here is (1) to provide a complete modeling of Note the remarkable agreement between spectroscopic and the system based on more appropriate stellar models (i.e. in- photographic determinations of the mass fraction. A weighted cluding microscopic diffusion) and (2) to propose a calibration average of the photographic and spectroscopic values leads to: of the unknown parameters (age, helium, individual masses) B85 Peg = 0:44 0:02: that fulfills the recent observational constraints. The paper is divided as follows. In Sect. 2, we collect and With the sum of masses and mass fraction derived above, the discuss the observational constraints. Section 3 is devoted to masses of the components are respectively: the description of physics and modeling. We summarize and mA = 0:84 0:08 M ; mB = 0:66 0:07 M ; conclude in Sect. 4. showing 85 Peg A definitively to be the more massive star. 2. Observations of the visual binary 85 Peg 2.2. Spectroscopic and photometric data 2.1. Astrometric data Stellar parameters were determined from spectroscopic and photometric analysis. Table 2 lists recently published data for For 85 Peg we are in the fortunate position of having two the photometry, effective temperature and metallicity of 85 Peg. precise, self consistent and independent determinations of the For 85 Peg A we chose to retain the recent determinations trigonometrical parallax and improved orbital elements; from Fe = − : ff = [ H ] 0 69 dex and Te A 5550 K of van’t Veer (2000). these data individual masses mA and mB can be derived inde- A This T ff determination relies on the careful fit of Balmer pendently. Table 1 shows the excellent agreement of the rel- e line profiles with Kurucz’s (1991) atlas model atmospheres evant elements of the astrometric orbits of Hall (1948) and with the constraint that the model reproduces both the Hα S¨oderhjelm (1999). The first determination of the parallax is and Hβ profiles. Furthermore we point out that, according to the standard photographic parallax (Wyller 1956; Heintz 1993) Th´evenin & Idiart (1999), the metallicity of metal-poor stars, based on improved orbit and several decades of photographic computed using model atmospheres in the lte approxima- long focus observations: the absolute photographic parallax 00 00 tion is underestimated by about 0.12 dex at the metallicity of amounts to $ = 0: 0798 0: 0033 (Heintz 1993). The abs 85 Peg. This is particularly important for the stellar position second determination is the recently improved adjustment of on the hr diagram (Lebreton et al. 1999). We take into ac- parallax and orbital elements by S¨oderhjelm (1999) based count this correction and adopt the value [ Fe ] = −0:57 0:11 on the Hipparcos 3.25 yr data and old ground-based observa- H A 00 00 (Th´evenin 2001). The α-elements (Mg, Ca, Si, Na, Al, Ti) tions yielding $ = 0: 0825 0: 0008. With the orbit of abs have been found to be enriched with respect to the Sun in Hall (1948) and the parallax of Heintz (1993) we derive the 85 Peg A (Fuhrmann 1998; van’t Veer 2000; Fulbright 2000). In sum of masses S = 1:63 0:33 M .Usingthedatafrom 85 Peg our calculations we take account of an α-elements enrichment, S¨oderhjelm (1999) we obtain S = 1:49 0:09 M .Forthe 85 Peg [α/Fe] =+0:40 dex, through appropriate opacities and input sum of masses we adopt the weighted average value: mixture. We computed the effective temperature of 85 Peg B Fe using the calibrations Teff = Teff {color; [ ]} from Lejeune S85 Peg = 1:50 0:09 M : H et al.
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